Problem

Source: 2012 Indonesia Round 2 TST 2 Problem 3

Tags: inequalities unsolved, inequalities



Let a1,a2,,an,b1,b2,,bn be positive reals such that a1+b1=a2+b2=+an+bn and na1a2anb1b2bnn. Prove that na1a2anb1b2bna1+a2++anb1+b2++bn.